2. Background theory

the earth at certain frequency ranges. Data are recorded as time series in two-way time (TWT) manner which after processing can be converted into depth domain by adding the velocity model during processing. Figure 1 shows the georadar instru-

Due to the ability of detecting shallow object with high resolution, georadar has been applied in many fields with various objectives. Georadar is able to distinguish two different objects based on different electrical properties; hence, georadar are commonly used in various field such as environment study, mining, ground water, ancient artifact, and others. Not only able to detect the electrical properties contrast of material, but also georadar is able to detect the subsurface structure like faults and folds. Hence, the application of georadar for detecting the subsurface structures and monitoring of active faults for mitigation purposes are promising, especially for unstable area in the urban/suburban area with high population where other active

The exact location of an active fault in urban area is very important to be known

Lembang fault is an example for active fault across urban area with high population density in Bandung, Indonesia. In this area, there are not less than 8 million people leaving around the Lembang fault. The length of this fault itself is about 29 km from east to west part of Bandung [3] as illustrated in Figure 2. Because of the compression system in this area, it is predicted that a huge accumulated energy is concentrated in this fault and potentially can be released any time as an earthquake. The earthquake then is predicted also which leads to trigger the local land-

Due to some reasons such as soil stability and environmental concern, techniques such as seismic refraction and seismic reflection that use dynamite explosion as a source, are not allowed. Hence the use of georadar technique for identifying

for the mitigation purposes. Hence, the potential landslide due to the unstable structure of this area can be warned early to avoid serious hazard or disaster. Many techniques have been used to monitor the stability and mitigate the potential landslide in the area around the active fault which is across the urban area. Nondestructive geophysical methods such as electrical method and electromagnetic method are commonly selected for the investigation and evaluation of the subsurface structure this area. Geo-penetrating radar (GPR) or georadar method is also a common geophysical method that is applied to understand the bedding subsurface and

ment and example of recorded data.

structure in the high-risk area in such condition.

(a) Georadar instrument [2], (b) example of recorded subsurface data.

source is prohibited.

Earth Crust

slide in this area.

Figure 1.

48

### 2.1 Georadar wave propagation

Georadar technique is developed based on electromagnetic wave propagation theory. In one dimension (1D), the propagation of electromagnetic wave in z-direction is explained by Maxwell equation:

$$\frac{\partial^2 E}{\partial \mathbf{z}^2} = \mu \varepsilon \frac{\partial^2 E}{\partial t^2} \tag{1}$$

The propagation of the electromagnetic wave is perpendicular to the electrical field (E) and magnetic field (H) and controlled by the velocity and attenuation of medium. The properties of medium are also related to the mineral composition and also water saturation of medium. The velocity of wave propagation in the medium depends on the velocity of electromagnetic wave in the vacuum (c = 0.3 m/ns), relative dielectric constant (εr), and relative magnetic permeability (μ<sup>r</sup> ¼ 1 for nonmagnetic material):

$$V\_m = c / \left\{ (\varepsilon\_r \mu\_r/2) \left[ \left( \mathbf{1} + P^2 \right) + \mathbf{1} \right] \right\}^{1/2} \tag{2}$$

where P ¼ σ=ωε is an absorption factor and σ is conductivity of medium, ϖ ¼ 2πf, where f is frequency and ε ¼ εrε<sup>o</sup> is vacuum permittivity (8.854 � <sup>10</sup>�<sup>12</sup> F/m). For the material with low loss, P� 0, the velocity of georadar is

$$V\_m = c/\sqrt{\varepsilon\_r} = 0.3/\sqrt{\varepsilon\_r}$$

Recording of georadar data is based on the reflection responses of dielectric contrast of medium. If dielectric contrast in the interface between different layers is strong, the reflectors have a strong amplitude in the georadargram. The strength of reflection (reflection coefficient R) is determined by the contrast of velocity and relative dielectric of medium at the boundary. The number of reflected energy is proportional to R:

$$R = \frac{(V\_1 - V\_2)}{(V\_1 + V\_2)} \text{ or } R = \frac{\sqrt{\varepsilon\_2} - \sqrt{\varepsilon\_1}}{\sqrt{\varepsilon\_2} - \sqrt{\varepsilon\_1}} \tag{3}$$

<sup>ε</sup> <sup>∗</sup> <sup>¼</sup> <sup>ε</sup> 0 þ i ε 00

is static or DC conductivity, while the complex conductivity is

where ω is angular frequency.

using a simple relation, V ¼ c= ffiffiffiffi

predicted or vice versa.

tomography (Figure 3).

coefficient [5].

51

2.3 Data processing

constant and porosity (ϕ) is defined as

DOI: http://dx.doi.org/10.5772/intechopen.85397

<sup>σ</sup> <sup>∗</sup> <sup>¼</sup> <sup>σ</sup> 0 þ iσ 00

εr

2.2 Configuration and resolution of georadar survey

velocity in the air, the velocity of georadar in the medium is defined as

þ σs=ωε<sup>o</sup>

where ε\* is a complex permittivity, ε" is an imaginary part of permittivity, and σ<sup>s</sup>

Identification of Active Faults in Landslide-Prone Regions Using Ground-Penetrating Radar…

In the porous medium material where water is a saturant, the bulk dielectric

where ε<sup>m</sup> and ε<sup>w</sup> are dielectric constant of matrix and water, respectively. By

Eq. (9) shows that if velocity can be extracted, then porosity of medium can be

Effectiveness and recoverable of georadar survey is determined by the configuration of the survey. At least there are two types of acquisition: monostatic mode and bistatic mode. In the monostatic mode, one antenna is used as transmitter

The vertical resolution of georadar is defined by its frequency or wavelength. Each antenna of georadar is designed for certain frequency range, where the peak energy will be associated in the peak frequency of the signal. Hence the vertical resolution georadar signal is determined by wavelength divide by four (λ/4). Meanwhile, the horizontal resolution of georadar is controlled mainly by the number of traces/s (or traces/m), the beam width, the radar cross section of the reflector, and the depth where target is located [4]. The conical beam of georadar signal itself is inversely proportional to the square root of attenuation coefficient (√α). It means that the horizontal resolution is better in the medium with high attenuation

Data processing in radargram depends on the objectives; there is no standard processing workflow. However, usually the processing data is done to gain the signal which is attenuated during propagation, removing some noise by filtering, deconvolution, and diffraction reduction through migration process. For certain purposes, sometimes the conversion from time domain needs to be done to get the

depth domain; in this case the velocity model is needed.

and receiver simultaneously. While in the bistatic mode, the receiver and transmitter are separated using different antenna. Based on the target itself, the configuration of data acquisition can be performed using different ways: radar reflection profiling, wide-angle reflection and reflection (WARR) and common midpoint (CMP) sounding, and transillumination or

� � (6)

<sup>¼</sup> <sup>j</sup>ωεo<sup>ε</sup> <sup>∗</sup> (7)

ε<sup>r</sup> ¼ ð Þ 1 � ϕ ε<sup>m</sup> þ ϕε<sup>w</sup> (8)

p , for low loss material where c is georadar wave

V ¼ c=½ � ð Þ 1 � ϕ ε<sup>m</sup> þ ϕε<sup>w</sup> (9)

where v1 and v2 are wave velocity of georadar at first and second layers and ε<sup>1</sup> and ε<sup>2</sup> are relative dielectric constant at first and second layers, respectively.

The energy loss during wave propagation is determined by some factors: antenna, transmission between air and soil, reduction due to the configuration or distance between transmitter and receiver, attenuation, and diffraction due to the sharp object. The energy reduction due to the wave propagation between transmitter and receiver is proportional to 1/r<sup>2</sup> , where the r is distance measured between source/antenna and receiver (another antenna), attenuation factor which defend on the dielectric properties of medium, and its magnetic and electrical field itself in the medium. Amplitude will be reduced in the depth of penetration due to the attenuation which is proportional to 1/e (about 37%) of initial energy which also called as skin depth. The skin depth depends on soil resistivity. The ratio of two different amplitudes is formulated as

$$E\_o/E\_x = \exp\left(-a\mathbf{x}\right) \tag{4}$$

where α is attenuation coefficient

$$a = \alpha \left\{ \left( \frac{\mu \varepsilon}{2} \right) \left[ \left( \mathbf{1} + \frac{\sigma^2}{\alpha^2 \varepsilon^2} \right)^{1/2} - \mathbf{1} \right] \right\}^{1/2} \tag{5}$$

Loss factor (P) = σ/ωϵ = tan D and skin depth is defined as

$$\delta = \mathbf{1}/a$$

If D < <1, δ ¼ ð Þ 2=σ ð Þ ε=μ 1=2 , the skin depth is formulated:

$$\delta = (\mathbf{5.31\sqrt{\varepsilon\_r}})/\sigma$$

where σ is an electrical conductivity (mS/m).

In the saturated porous medium, the loss energy is proportional to the conductivity and invers proportionally to the relative dielectric constant and frequency. The conductivity and relative dielectric constant is dominated by fluid saturant compared to the matrix itself. The bulk of relative dielectric constant (εr) is roughly equal to porosity and relative dielectric constant of fluid (εr). Due to the fluid/saturant is more conductive, the attenuation becomes higher. The geological material mostly have a relative dielectrical constant is about 3–30, and hence the georadar wave velocity is about 0.06–0.175 m/ns, while the air velocity is 299.8 mm/ns.

The relationship between dielectric, permittivity, and conductivity of medium is governed by

Identification of Active Faults in Landslide-Prone Regions Using Ground-Penetrating Radar… DOI: http://dx.doi.org/10.5772/intechopen.85397

$$
\boldsymbol{\varepsilon}^\* = \boldsymbol{\varepsilon}^\prime + \dot{\boldsymbol{\varepsilon}} \left( \boldsymbol{\varepsilon}^\prime + \sigma\_\circ / \rho \mathbf{e}\_\sigma \right) \tag{6}
$$

where ε\* is a complex permittivity, ε" is an imaginary part of permittivity, and σ<sup>s</sup> is static or DC conductivity, while the complex conductivity is

$$
\sigma^\* = \sigma' + i\sigma'' = ja\epsilon\_o\varepsilon^\* \tag{7}
$$

where ω is angular frequency.

Vm <sup>¼</sup> <sup>c</sup><sup>=</sup> ffiffiffiffi

<sup>R</sup> <sup>¼</sup> ð Þ <sup>V</sup><sup>1</sup> � <sup>V</sup><sup>2</sup> ð Þ V<sup>1</sup> þ V<sup>2</sup>

proportional to R:

Earth Crust

ter and receiver is proportional to 1/r<sup>2</sup>

where α is attenuation coefficient

If D < <1, δ ¼ ð Þ 2=σ ð Þ ε=μ

299.8 mm/ns.

governed by

50

<sup>α</sup> <sup>¼</sup> <sup>ω</sup> με

2 � �

Loss factor (P) = σ/ωϵ = tan D and skin depth is defined as

1=2

where σ is an electrical conductivity (mS/m).

amplitudes is formulated as

εr <sup>p</sup> <sup>¼</sup> <sup>0</sup>:3<sup>=</sup> ffiffiffiffi

Recording of georadar data is based on the reflection responses of dielectric contrast of medium. If dielectric contrast in the interface between different layers is strong, the reflectors have a strong amplitude in the georadargram. The strength of reflection (reflection coefficient R) is determined by the contrast of velocity and relative dielectric of medium at the boundary. The number of reflected energy is

or R ¼

where v1 and v2 are wave velocity of georadar at first and second layers and ε<sup>1</sup>

source/antenna and receiver (another antenna), attenuation factor which defend on the dielectric properties of medium, and its magnetic and electrical field itself in the medium. Amplitude will be reduced in the depth of penetration due to the attenuation which is proportional to 1/e (about 37%) of initial energy which also called as skin depth. The skin depth depends on soil resistivity. The ratio of two different

> <sup>1</sup> <sup>þ</sup> <sup>σ</sup><sup>2</sup> ω<sup>2</sup>ε<sup>2</sup> � �<sup>1</sup>=<sup>2</sup>

δ ¼ 1=α

<sup>δ</sup> <sup>¼</sup> <sup>5</sup>:<sup>31</sup> ffiffiffiffi

In the saturated porous medium, the loss energy is proportional to the conductivity and invers proportionally to the relative dielectric constant and frequency. The conductivity and relative dielectric constant is dominated by fluid saturant compared to the matrix itself. The bulk of relative dielectric constant (εr) is roughly equal to porosity and relative dielectric constant of fluid (εr). Due to the fluid/saturant is more conductive, the attenuation becomes higher. The geological material mostly have a relative dielectrical constant is about 3–30, and hence the georadar wave velocity is about 0.06–0.175 m/ns, while the air velocity is

, the skin depth is formulated:

εr <sup>p</sup> ð Þ=<sup>σ</sup>

The relationship between dielectric, permittivity, and conductivity of medium is

( ) " # <sup>1</sup>=<sup>2</sup>

and ε<sup>2</sup> are relative dielectric constant at first and second layers, respectively. The energy loss during wave propagation is determined by some factors: antenna, transmission between air and soil, reduction due to the configuration or distance between transmitter and receiver, attenuation, and diffraction due to the sharp object. The energy reduction due to the wave propagation between transmit-

εr p

ffiffiffiffi ε2 <sup>p</sup> � ffiffiffiffi ε1 p

ffiffiffiffi ε2 <sup>p</sup> � ffiffiffiffi ε1

p (3)

(5)

, where the r is distance measured between

Eo=Ex ¼ exp ð Þ �αx (4)

� 1

In the porous medium material where water is a saturant, the bulk dielectric constant and porosity (ϕ) is defined as

$$
\varepsilon\_r = (\mathbf{1} - \phi)\varepsilon\_m + \phi\varepsilon\_w \tag{8}
$$

where ε<sup>m</sup> and ε<sup>w</sup> are dielectric constant of matrix and water, respectively. By using a simple relation, V ¼ c= ffiffiffiffi εr p , for low loss material where c is georadar wave velocity in the air, the velocity of georadar in the medium is defined as

$$\mathbf{V} = \mathbf{c} / [(\mathbf{1} - \phi)\varepsilon\_m + \phi \varepsilon\_w] \tag{9}$$

Eq. (9) shows that if velocity can be extracted, then porosity of medium can be predicted or vice versa.

#### 2.2 Configuration and resolution of georadar survey

Effectiveness and recoverable of georadar survey is determined by the configuration of the survey. At least there are two types of acquisition: monostatic mode and bistatic mode. In the monostatic mode, one antenna is used as transmitter and receiver simultaneously. While in the bistatic mode, the receiver and transmitter are separated using different antenna. Based on the target itself, the configuration of data acquisition can be performed using different ways: radar reflection profiling, wide-angle reflection and reflection (WARR) and common midpoint (CMP) sounding, and transillumination or tomography (Figure 3).

The vertical resolution of georadar is defined by its frequency or wavelength. Each antenna of georadar is designed for certain frequency range, where the peak energy will be associated in the peak frequency of the signal. Hence the vertical resolution georadar signal is determined by wavelength divide by four (λ/4). Meanwhile, the horizontal resolution of georadar is controlled mainly by the number of traces/s (or traces/m), the beam width, the radar cross section of the reflector, and the depth where target is located [4]. The conical beam of georadar signal itself is inversely proportional to the square root of attenuation coefficient (√α). It means that the horizontal resolution is better in the medium with high attenuation coefficient [5].

#### 2.3 Data processing

Data processing in radargram depends on the objectives; there is no standard processing workflow. However, usually the processing data is done to gain the signal which is attenuated during propagation, removing some noise by filtering, deconvolution, and diffraction reduction through migration process. For certain purposes, sometimes the conversion from time domain needs to be done to get the depth domain; in this case the velocity model is needed.

where t is travel time, A is attenuation factor, B is spherical divergence factor,

In the implementation on processing, programmed gain control (PGC) and automated gain control (AGC) are commonly used. In the PGC, the gain function is estimated by interpolating the amplitude at certain window sample. While in the AGC, the gain function is generated by taking root mean square (RMS) on each amplitude at certain window. The gain function g(t) is interpolated in the central of the selected window. The window length selection affects the reflector strength in the result. If the window length is too wide, the signal from deeper part will gain less, and if selected window is too small, all the reflection will be gained strongly; in this case it is difficult to distinguish strong reflector from others because all reflector

Identification of Active Faults in Landslide-Prone Regions Using Ground-Penetrating Radar…

The velocity analysis needs to be conducted to know the value of velocity (velocity model); hence, the true depth and slope can be estimated. Direct measurement of medium velocity can be done from wellbore or indirectly through velocity analysis during normal moveout (NMO) process. The NMO process is

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x 2 � �<sup>2</sup> <sup>þ</sup> <sup>h</sup><sup>2</sup>

> > ð Þþ <sup>0</sup> <sup>x</sup><sup>2</sup> V2

<sup>V</sup> (11)

=V2

ð Þ¼ <sup>0</sup> 4h2

q

4h<sup>2</sup> <sup>V</sup><sup>2</sup> , if T<sup>2</sup>

<sup>V</sup><sup>2</sup> <sup>þ</sup>

ð Þ¼ <sup>x</sup> <sup>T</sup><sup>2</sup>

where V is velocity obtained from relation of reflection time at zero offset and

Geological of Bandung area is still young and renewed because of volcanic activities around Bandung area. Based on previous study, there is a Lembang fault in Bandung area which occurred from tectonic process. This fault located in the

and C is gain constant.

Figure 4.

will be gained strongly.

illustrated in Figure 4:

offset and distance/offset.

53

The function of NMO is describes as follows:

Schematic of transmitter and receiver related to the NMO process.

DOI: http://dx.doi.org/10.5772/intechopen.85397

4 <sup>x</sup><sup>2</sup> <sup>4</sup> <sup>þ</sup> <sup>h</sup><sup>2</sup> � �

<sup>T</sup><sup>2</sup> <sup>¼</sup>

3. Acquisition and processing data

<sup>T</sup> <sup>¼</sup> <sup>2</sup><sup>S</sup> <sup>V</sup> <sup>¼</sup> <sup>2</sup>

<sup>V</sup><sup>2</sup> <sup>¼</sup> <sup>x</sup><sup>2</sup>

Then T<sup>2</sup>

Figure 3.

(A) Sounding WARR dan, (B) sounding CMP, (C) graph of time-offset (T-X) with NMO, (D) graph of relationship T2–X2 [3].

Gain is performed to amplify the amplitude decay due to the distance of propagation. Factors affecting the amplitude decay are attenuation and spherical divergence propagation. Gain is performed by applying a gain function g(t):

$$\text{Gain} \,\left(\text{dB}\right) = \text{A.t} + \text{B.20} \,\log\left(\text{t}\right) + \text{C} \tag{10}$$

Identification of Active Faults in Landslide-Prone Regions Using Ground-Penetrating Radar… DOI: http://dx.doi.org/10.5772/intechopen.85397

Figure 4.

Schematic of transmitter and receiver related to the NMO process.

where t is travel time, A is attenuation factor, B is spherical divergence factor, and C is gain constant.

In the implementation on processing, programmed gain control (PGC) and automated gain control (AGC) are commonly used. In the PGC, the gain function is estimated by interpolating the amplitude at certain window sample. While in the AGC, the gain function is generated by taking root mean square (RMS) on each amplitude at certain window. The gain function g(t) is interpolated in the central of the selected window. The window length selection affects the reflector strength in the result. If the window length is too wide, the signal from deeper part will gain less, and if selected window is too small, all the reflection will be gained strongly; in this case it is difficult to distinguish strong reflector from others because all reflector will be gained strongly.

The velocity analysis needs to be conducted to know the value of velocity (velocity model); hence, the true depth and slope can be estimated. Direct measurement of medium velocity can be done from wellbore or indirectly through velocity analysis during normal moveout (NMO) process. The NMO process is illustrated in Figure 4:

The function of NMO is describes as follows:

$$T = \frac{2S}{V} = \frac{2\sqrt{\left(\frac{\mathbf{x}}{2}\right)^2 + h^2}}{V} \tag{11}$$

$$T^2 = \frac{4\left(\frac{\mathbf{x}^2}{4} + h^2\right)}{V^2} = \frac{\mathbf{x}^2}{V^2} + \frac{4h^2}{V^2}, \text{if } \mathbf{T}^2(\mathbf{0}) = 4\mathbf{h}^2/\mathbf{V}^2$$

$$\text{Then } T^2(\mathbf{x}) = T^2(\mathbf{0}) + \frac{\mathbf{x}^2}{V^2}$$

where V is velocity obtained from relation of reflection time at zero offset and offset and distance/offset.

### 3. Acquisition and processing data

Geological of Bandung area is still young and renewed because of volcanic activities around Bandung area. Based on previous study, there is a Lembang fault in Bandung area which occurred from tectonic process. This fault located in the

Gain is performed to amplify the amplitude decay due to the distance of propagation. Factors affecting the amplitude decay are attenuation and spherical diver-

(A) Sounding WARR dan, (B) sounding CMP, (C) graph of time-offset (T-X) with NMO, (D) graph of

Gain dB ð Þ¼ A:t þ B:20 log tð Þþ C (10)

gence propagation. Gain is performed by applying a gain function g(t):

Figure 3.

Earth Crust

52

relationship T2–X2 [3].

southern part of Lembang and crossing Cisarua from east to west of Manglayang mountain. Throw of this fault is varying up to 450 m in Pulasari near to the target area. The Lembang fault was created during the Pleistosen era (about 500,000 years ago) [6].

In the end of Miocene, series of mountains and folds are created in the northern part and in the southern part which become series of volcanos. In the breaking time of Pliocene era, there is no activity of volcanoes and sedimentation, and in the end of Pliocene era, series of mountains were created, and sediments in the northern part were folded and shifted into northern part of Bandung. Materials as a result of volcano eruption activities are distributed into southern part of Bandung.

domain into depth domain in the profile. In general, the velocity is quite high because the lithology is dominated by tuff, andesite, and breccia volcanic.

Velocity model extracted from hyperbole fitting curve during velocity analysis.

Depth (m) Velocity (m/μs) 15.63 196.17 17.16 186.37 22.25 180.69

Identification of Active Faults in Landslide-Prone Regions Using Ground-Penetrating Radar…

Out of several profiles which were studied, profile 03 displayed the large fault in the radargram which is associated with a main Lembang fault. In the other profiles, there are some small fault systems. Based on the velocity analysis, the structure of Lembang fault is a conductive area where the velocity decreases with depth. Profile in Figure 6 which is taken perpendicular to the fault shows a normal fault system. The foot wall is located in the northern part and hanging wall in the southern part. The position of foot wall part is lower about 7–8 m compared to the hanging wall part. The structure of this area consists of basement which is indicated by a free reflection area and sediment bedding in the horizontal layer. Above the foot wall

In Figure 6, the top of basement formation is interpreted as the blue line indicates a normal fault. The folded reflection can be resulted as post fault due to the compression from the northern part; the horizontal bedding is folded as small anticline. Cracking in the shoulder of road around this profile indicates that the fault reaches the surface. Those crack lies in the west–east direction where the northern part is lower than southern part. Previous study mentioned that this active

4. Result and discussion

DOI: http://dx.doi.org/10.5772/intechopen.85397

Table 2.

Figure 6.

55

Cross section taken perpendicular to the fault.

part, there is a pattern of unconformity.

To detect the existence of Lembang fault, a georadar survey was conducted in this area. Sketch of data gathering in this area is shown in Figure 5. The data collection was conducted using common-offset method with 25 and 50 MHz antenna. Most of the profile was selected perpendicular to the fault.

All the data are processed using Seismic Unix (SU) software by performing the scaling on the time sampling rate from nanosecond to millisecond (ms), frequency from megahertz to hertz and velocity from m/ns to m/μs. The details of conversion factor are shown in Table 1.

The processing data includes filtering using band-pass filter (10, 20, 30, 50) MHz for antenna 25 MHz and (10, 30, 70, 100) MHz for 50 Hz, AGC, and velocity analysis based on hyperbole fitting curve. The velocity obtained from hyperbole fitting curve is shown in Table 2. This velocity model was used to convert time
